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Apologies but I have difficulty expressing this in words; what I want to do is evenly, with the edges parallel, 'thicken' a selection of faces/planes.

I have used the solidify modifier, but for some reason this makes the topology look weird, as though it's sloped.

enter image description here

The object in the top part of the image displays what I would like, but to be applied to the bottom object. The red drawing on the bottom shows the cross section of the object when the solidifiy modifier is applied to it, whereas the green drawing shows how I would like it to look.

I would like to know if there is a way to achieve this not just for a circular object, but any selection of planes.

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The solidify modifier works with the normals of the plains, so that sloped effect is normal (both expression wise and technically). One way you could solve this particular ring is simply do an extrusion with zero transform, and then scale the extruded geometry along the X and y axes. How to do this with “any selection of faces,” however, largely depends on what rules those faces would and would not be following. Do they remain in a band-like, edge-to-edge shape, even if it’s not a circle? Do they always tilt by the same amount together? Is the band always at an even height? Is it always concave? What you should do in any particular situation is a matter of engineering, and it requires more Help than this site can give, practically at least.

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